Failure of universal finite-size scaling above the upper critical dimension

X.S. Chen and V. Dohm

Physica A: Statistical Mechanics and its Applications, 1998, vol. 251, issue 3, 439-451

Abstract: Previous theories have predicted that O(n) symmetric systems in a finite cubic geometry with periodic boundary conditions have universal finite-size scaling functions near criticality in d>4 dimensions. On the basis of exact results for the O(n) symmetric ϕ4 model in the large n limit we show that universal finite-size scaling does not hold in the predicted form because of significant cut-off and lattice effects for d>4. It is shown that finite-size scaling is valid with two reference lengths which turn out to be identical with the amplitudes of the bulk correlation length. For the ϕ4 field theory the finite-size scaling functions are shown to be non-universal, i.e., to depend explicitly on the cut-off and on the bare four-point coupling constant, whereas for a ϕ4 lattice model the finite-size scaling functions have a different form that is independent of the lattice spacing and the four-point coupling constant.

Keywords: Finite-size scaling; ϕ4 field theory; Universality (search for similar items in EconPapers)
Date: 1998
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437197006882
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:251:y:1998:i:3:p:439-451

DOI: 10.1016/S0378-4371(97)00688-2

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().